Plastic Cup is making shadows inside of itself that cannot be removed
This is a smoothing issue. In Data Properties, under Normals, enable Autosmooth.

You shaded your object smooth cause you didn't want to see the verticals faces as individual faces, but as a curved surface. The smoothing is done (more or less) by averaging the normal between two faces, and it works really well on the side of the cylinder. But it also average the normals between the bottom and the side faces, and betwen the "collar" and the side, which looks quite ugly.

Autosmooth smooth the faces below a specific angle (30° by default), and keep sharp the edge between faces above that angle.